Add pascals-triangle (#276)

config.json

@@ -500,6 +500,14 @@
         "prerequisites": [],
         "difficulty": 4
       },
+      {
+        "slug": "pascals-triangle",
+        "name": "Pascal's Triangle",
+        "uuid": "4bf78b97-f958-4327-bdbb-f36dcd6c7f15",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 6
+      },
       {
         "slug": "pig-latin",
         "name": "Pig Latin",

exercises/practice/pascals-triangle/.docs/hints.md

@@ -0,0 +1,6 @@
+# Hints
+
+## General
+
+- The `$t0-9` registers can be used to temporarily store values
+- The instructions specify which registers are used as input and output

exercises/practice/pascals-triangle/.docs/instructions.append.md

@@ -0,0 +1,10 @@
+# Instructions append
+
+## Registers
+
+| Register | Usage        | Type    | Description             |
+| -------- | ------------ | ------- | ----------------------- |
+| `$a0`    | input        | integer | number of triangle rows |
+| `$a1`    | input/output | address | array of words          |
+| `$v0`    | output       | integer | number of output words  |
+| `$t0-9`  | temporary    | any     | for temporary storage   |

exercises/practice/pascals-triangle/.docs/instructions.md

@@ -0,0 +1,35 @@
+# Instructions
+
+Your task is to output the first N rows of Pascal's triangle.
+
+[Pascal's triangle][wikipedia] is a triangular array of positive integers.
+
+In Pascal's triangle, the number of values in a row is equal to its row number (which starts at one).
+Therefore, the first row has one value, the second row has two values, and so on.
+
+The first (topmost) row has a single value: `1`.
+Subsequent rows' values are computed by adding the numbers directly to the right and left of the current position in the previous row.
+
+If the previous row does _not_ have a value to the left or right of the current position (which only happens for the leftmost and rightmost positions), treat that position's value as zero (effectively "ignoring" it in the summation).
+
+## Example
+
+Let's look at the first 5 rows of Pascal's Triangle:
+
+```text
+    1
+   1 1
+  1 2 1
+ 1 3 3 1
+1 4 6 4 1
+```
+
+The topmost row has one value, which is `1`.
+
+The leftmost and rightmost values have only one preceding position to consider, which is the position to its right respectively to its left.
+With the topmost value being `1`, it follows from this that all the leftmost and rightmost values are also `1`.
+
+The other values all have two positions to consider.
+For example, the fifth row's (`1 4 6 4 1`) middle value is `6`, as the values to its left and right in the preceding row are `3` and `3`:
+
+[wikipedia]: https://en.wikipedia.org/wiki/Pascal%27s_triangle

exercises/practice/pascals-triangle/.docs/introduction.md

@@ -0,0 +1,22 @@
+# Introduction
+
+With the weather being great, you're not looking forward to spending an hour in a classroom.
+Annoyed, you enter the class room, where you notice a strangely satisfying triangle shape on the blackboard.
+Whilst waiting for your math teacher to arrive, you can't help but notice some patterns in the triangle: the outer values are all ones, each subsequent row has one more value than its previous row and the triangle is symmetrical.
+Weird!
+
+Not long after you sit down, your teacher enters the room and explains that this triangle is the famous [Pascal's triangle][wikipedia].
+
+Over the next hour, your teacher reveals some amazing things hidden in this triangle:
+
+- It can be used to compute how many ways you can pick K elements from N values.
+- It contains the Fibonacci sequence.
+- If you color odd and even numbers differently, you get a beautiful pattern called the [Sierpiński triangle][wikipedia-sierpinski-triangle].
+
+The teacher implores you and your classmates to lookup other uses, and assures you that there are lots more!
+At that moment, the school bell rings.
+You realize that for the past hour, you were completely absorbed in learning about Pascal's triangle.
+You quickly grab your laptop from your bag and go outside, ready to enjoy both the sunshine _and_ the wonders of Pascal's triangle.
+
+[wikipedia]: https://en.wikipedia.org/wiki/Pascal%27s_triangle
+[wikipedia-sierpinski-triangle]: https://en.wikipedia.org/wiki/Sierpi%C5%84ski_triangle

exercises/practice/pascals-triangle/.meta/config.json

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "keiravillekode"
+  ],
+  "files": {
+    "solution": [
+      "impl.mips"
+    ],
+    "test": [
+      "runner.mips"
+    ],
+    "example": [
+      ".meta/example.mips"
+    ]
+  },
+  "blurb": "Compute Pascal's triangle up to a given number of rows.",
+  "source": "Pascal's Triangle at Wolfram Math World",
+  "source_url": "https://www.wolframalpha.com/input/?i=Pascal%27s+triangle"
+}

exercises/practice/pascals-triangle/.meta/example.mips

@@ -0,0 +1,50 @@
+# | Register | Usage        | Type    | Description                      |
+# | -------- | ------------ | ------- | -------------------------------- |
+# | `$a0`    | input        | integer | number of triangle rows          |
+# | `$a1`    | input/output | address | start of array of words          |
+# | `$v0`    | output       | integer | number of output words           |
+# | `$t0`    | temporary    | address | output pointer                   |
+# | `$t1`    | temporary    | integer | number of bytes in $a0 words     |
+# | `$t2`    | temporary    | integer | row length, in bytes             |
+# | `$t3`    | temporary    | address | pointer into previous row        |
+# | `$t4`    | temporary    | address | initial 1 of current row         |
+# | `$t5`    | temporary    | address | final 1 of current row           |
+# | `$t6`    | temporary    | integer | left value from previous row     |
+# | `$t7`    | temporary    | integer | right value from previous row    |
+# | `$t8`    | temporary    | integer | sum two values from previous row |
+
+.globl rows
+
+rows:
+        move    $t0, $a1                # output pointer
+        beqz    $a0, done               # stop immediately if 0 rows
+        sll     $t1, $a0, 2             # number of bytes in $a0 words
+        move    $t2, $zero              # row length, in bytes
+        li      $t7, 1                  # value for first row
+
+next_row:
+        move   $t4, $t0                 # address of initial 1 of current row
+        add    $t5, $t0, $t2            # address of final 1 of current row
+        addi   $t2, $t2, 4              # row length, in bytes
+        move   $t6, $zero               # left value from previous row
+        beq    $t0, $t5, last_column
+
+next_column:
+        lw     $t7, 0($t3)              # read from previous row
+        addi   $t3, $t3, 4
+        add    $t8, $t6, $t7            # sum two values from previous row
+        move   $t6, $t7
+        sw     $t8, 0($t0)              # write output
+        addi   $t0, $t0, 4
+        bne    $t0, $t5, next_column
+
+last_column:
+        sw     $t7, 0($t0)              # write output
+        addi   $t0, $t0, 4
+        move   $t3, $t4                 # start of most recent row
+        bne    $t2, $t1, next_row       # repeat until we have final row length
+
+done:
+        sub    $v0, $t0, $a1            # subtract start of output
+        srl    $v0, $v0, 2              # convert to number of words
+        jr     $ra

exercises/practice/pascals-triangle/.meta/tests.toml

@@ -0,0 +1,34 @@
+# This is an auto-generated file.
+#
+# Regenerating this file via `configlet sync` will:
+# - Recreate every `description` key/value pair
+# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications
+# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion)
+# - Preserve any other key/value pair
+#
+# As user-added comments (using the # character) will be removed when this file
+# is regenerated, comments can be added via a `comment` key.
+
+[9920ce55-9629-46d5-85d6-4201f4a4234d]
+description = "zero rows"
+
+[70d643ce-a46d-4e93-af58-12d88dd01f21]
+description = "single row"
+
+[a6e5a2a2-fc9a-4b47-9f4f-ed9ad9fbe4bd]
+description = "two rows"
+
+[97206a99-79ba-4b04-b1c5-3c0fa1e16925]
+description = "three rows"
+
+[565a0431-c797-417c-a2c8-2935e01ce306]
+description = "four rows"
+
+[06f9ea50-9f51-4eb2-b9a9-c00975686c27]
+description = "five rows"
+
+[c3912965-ddb4-46a9-848e-3363e6b00b13]
+description = "six rows"
+
+[6cb26c66-7b57-4161-962c-81ec8c99f16b]
+description = "ten rows"

exercises/practice/pascals-triangle/impl.mips

@@ -0,0 +1,11 @@
+# | Register | Usage        | Type    | Description             |
+# | -------- | ------------ | ------- | ----------------------- |
+# | `$a0`    | input        | integer | number of triangle rows |
+# | `$a1`    | input/output | address | array of words          |
+# | `$v0`    | output       | integer | number of output words  |
+# | `$t0-9`  | temporary    | any     | for temporary storage   |
+
+.globl rows
+
+rows:
+        jr $ra